Bosonization and the eikonal expansion: similarities and differences

Details Bosonization and the eikonal expansion: similarities and differences Bosonization and the eikonal expansion: similarities and differences

1996-02-07

arxiv.org/abs/cond-mat/9602038v1

Int. J. Mod. Phys. B 10, 2111 (1996)

Physics

Condensed Matter

Revtex, one figure

Scientific paper

We compare two non-perturbative techniques for calculating the single-particle Green's function of interacting Fermi systems with dominant forward scattering: our recently developed functional integral approach to bosonization in arbitrary dimensions, and the eikonal expansion. In both methods the Green's function is first calculated for a fixed configuration of a background field, and then averaged with respect to a suitably defined effective action. We show that, after linearization of the energy dispersion at the Fermi surface, both methods yield for Fermi liquids exactly the same non-perturbative expression for the quasi-particle residue. However, in the case of non-Fermi liquid behavior the low-energy behavior of the Green's function predicted by the eikonal method can be erroneous. In particular, for the Tomonaga-Luttinger model the eikonal method neither reproduces the correct scaling behavior of the spectral function, nor predicts the correct location of its singularities.

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